# CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHERE Measurement CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHERE Measurement of atmospheric pressure with the mercury barometer: vacuum Atmospheric pressure P = PA = PB = Hg gh h A B Mean sea-level pressure: P = 1.013x105 Pa = 1013 hPa = 1013 mb = 1 atm = 760 mm Hg (torr) SEA LEVEL PRESSURE MAP THIS MORNING (2/4/14, 15Z)

and the forecast: weather.unisys.com SEA-LEVEL PRESSURE CANT VARY OVER MORE THAN A NARROW RANGE: 1013 50 hPa Consider a pressure gradient at sea level operating on an elementary air parcel dxdydz: P(x) P(x+dx) Pressure-gradient force Vertical area dydz Acceleration dF ( P( x) P( x dx))dydz

1 dP dx For P = 10 hPa over x = 100 km, ~ 10-2 m s-2 100 km/h wind in 3 h! Effect of wind is to transport air to area of lower pressure dampen P On mountains, however, the surface pressure is lower, and the pressure-gradient force along the Earth surface is balanced by gravity: P(z+z) P-gradient gravity P(z) This is why weather maps show sea level isobars even over land; the fictitious sea-level pressure assumes an air column to be present between the surface and sea level MASS ma OF THE ATMOSPHERE Mean pressure at Earth's surface: 984 hPa

Radius of Earth: 6380 km ma 4 R 2 PSurface g 18 5.13 10 kg Total number of moles of air in atmosphere: ma Na 1.8 1020 moles Ma Mol. wt. of air: 29 g mole-1 = 0.029 kg mole-1

QUESTIONS 1. What is the fractional increase in volume of water-soluble aerosol particles when relative humidity increases from 90% to 95%? (assume that the particles are mainly water, so neglect the contribution of the solute to particle volume). Assuming that visibility degradation is proportional to the cross-sectional area of the particles, what is the resulting percentage decrease in visibility? 2. Why does it take longer to boil an egg in Denver than in Boston? CLAUSIUS-CLAPEYRON EQUATION: PH2O, SAT = f(T) PH2O,SAT (hPa) PH 2O , SAT 1 1 A exp[ B ( )] T To

T (K) A = 6.11 hPa B = - 5310 K To = 273 K VERTICAL PROFILES OF PRESSURE AND TEMPERATURE Mean values for 30oN, March Stratopause Tropopause Barometric law (variation of pressure with altitude) Consider elementary slab of atmosphere: P(z+dz) P(z) unit area P( z ) P( z dz ) a gdz

PM a a RT Ideal gas law: dP Mag dz P RT dP a g

dz hydrostatic equation Assume T = constant, integrate: P( z ) P(0)e z/H RT with scale height H 7.4 km (T 250 K) Mag Barometric law na ( z ) na (0)e z/H

P( z ) P( z H ) ; e P( z ) P ( z 5km) 2 Application of barometric law: the sea-breeze effect